2003/07/09 by Laurent Nottale, Nottale, Laurent
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #Scientific Research and Discoveries #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.gr-qc/0307042
openalex publication_date 2003/07/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
An anomalous constant acceleration of (8.7 \± 1.3) x 10-8 cm/s2 directed\ntoward the Sun has been discovered by Anderson et al. in the motion of the\nPioneer 10/11 and Galileo spacecrafts. In parallel, the WMAP results have\ndefinitively established the existence of a cosmological constant Lambda=1/\nLU2, and therefore of an invariant cosmic length-scale LU=(2.72 \± 0.10)\nGpc. We show that the existence of this invariant scale definitively implements\nMach's principle in Einstein's theory of general relativity. Then we\ndemonstrate, in the framework of an exact cosmological solution of Einstein's\nfield equations which is valid both locally and globally, that the definition\nof inertial systems ultimately depends on this length-scale. As a consequence,\nusual local coordinates are not inertial, so that the motion of a free body of\nspeed v is expected to contain an additional constant acceleration\naP=v2( surd3 LU), which is, using the WMAP five years results, (6.02 \±\n0.34) x 10-8 cm/s2 when v \≈ c. Such an effect is too small to\ncontribute significantly to the Pioneer acceleration (since vPioneer \≈\n12 km/s << c), but could be possibly observed in a dedicated space mission.\n